The goal of this work is to implement the model of the playback interruptions for streaming services when the user downloads the video with ON/OFF strategy. We will develop a complete framework to compute starvation events during the video playback. In order to achieve these objectives, we model the users' dynamics by an M/M/1/K queuing model with exponential service time and Poison arrivals for the users. As the user joins a network randomly, we compute the probability of starvation events using ordinary differential equations: the user downloads the full video and leaves the network. This probability depends on several parameters that telecommunication operators can control, especially the start-up delay and the OFF duration.